But messaging and texting is so artificial.
Several options.
She may just be after free drinks and a meal, and so attractive she can count on that with no need for her to keep being interesting.
She may like you but be keeping her options open
She may be worrying about whether she's overinvesting in you, because she speaks to you almost every day-
She may be just looking forward to meeting you, and hope you don't just disappear like so many men do.
You haven't met her yet.
I repeat. you haven't met her yet
Men, in almost all situations, have to do the chasing. This is, unfortunately, the way of things. It would be lovely if women were as empowered to chase as men need to be, and men didn't get put off by it, but that is the way things are for the moment.
So yes, it's somewhat rude. But you haven't met her yet, you can afford to swallow a little pride to be friendly and funny and amazing, and then meet her and see if it's worth more.
(Sorry, I disagree with the majority of women on here, as I've been in Info's situation, trying to get a date with an attractive women. Most of you haven't. I've succeeded, and then usually I've found they're up themselves a bit. Not always, and those ones who aren't.. Well it's worth a bit of swallowed pride)